Generalized approximate message passing for cosparse analysis compressive sensing
Mark Borgerding, Philip Schniter, Jeremy P. Vila, Sundeep Rangan
Abstract
In cosparse analysis compressive sensing (CS), one seeks to estimate a non-sparse signal vector from noisy sub-Nyquist linear measurements by exploiting the knowledge that a given linear transform of the signal is cosparse, i.e., has sufficiently many zeros. We propose a novel approach to cosparse analysis CS based on the generalized approximate message passing (GAMP) algorithm. Unlike other AMP-based approaches to this problem, ours works with a wide range of analysis operators and regularizers. In addition, we propose a novel ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> -like soft-thresholder based on MMSE denoising for a spike-and-slab distribution with an infinite-variance slab. Numerical demonstrations on synthetic and practical datasets demonstrate advantages over existing AMP-based, greedy, and reweighted-ℓ <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> approaches.
BibTeX
@inproceedings{icassp2015_generalizedappro,
title = {Generalized approximate message passing for cosparse analysis compressive sensing},
author = {Mark Borgerding and Philip Schniter and Jeremy P. Vila and Sundeep Rangan},
booktitle = {ICASSP 2015},
year = {2015}
}